Abstract
The purpose of this article is to build a class of the best linear unbiased estimators (BLUE) of the linear parametric functions, to prove some necessary and sufficient conditions for their existence and to derive them from the corresponding normal equations, when a family of multivariate growth curve models is considered. It is shown that the classical BLUE known for this family of models is the element of a particular class of BLUE built in the proposed manner. The results are expressed in a convenient computational form by using the coordinate-free approach and the usual parametric representations.
Resumen
El propósito del artículo es construir una clase de estimadores lineales insesgados óptimos (BLUE) de funciones paramétricas lineales para demostrar algunas condiciones necesarias y suficientes para su existencia y deducirlas de las correspondientes ecuaciones normales, cuando se considera una familia de modelos con curva de crecimiento multivariante. Se demuestra que la clase de los BLUE conocidos para esta familia de modelos es un elemento de una clase particular de los BLUE que se construyen de esta manera. Los resultados se presentan en un formato computacional adecuado usando un enfoque que es independiente de las coordenadas y las representaciones paramétricas usuales.
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Beganu, G. Some properties of the best linear unbiased estimators in multivariate growth curve models. Rev. R. Acad. Cien. Serie A. Mat. 103, 161–166 (2009). https://doi.org/10.1007/BF03191848
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DOI: https://doi.org/10.1007/BF03191848